Question

BD bisects ABC. m ABD=2y m DBC=5y-12. What is ABC?

Answer 1

To find the measure of ABC, we can use the fact that BD bisects the triangle. By setting up an equation using the given angle measures, we can solve for the value of y and find the measure of ABC.

Step-by-step explanation:

Given that BD bisects ABC, we know that the angle ABD is equal to the angle DBC since the line BD acts as a dividing line. Let's set the values of these angles as 2y and 5y-12, respectively.

Since BD bisects ABC, the sum of angles ABD and DBC should equal 180 degrees. We can write the equation as follows: 2y + (5y-12) = 180.

Now, we can solve for y by combining like terms and simplifying the equation. Once we find the value of y, we can substitute it back into the expressions for each angle to determine their specific measures and obtain the value for ABC.

Answer 2

16

Step-by-step explanation:

The two angle created by the bisector have equal measures, so ...

m∠ABD = m∠DBC

2y = 5y -12

0 = 3y -12

0 = y -4

4 = y

2y = 2·4 = 8

m∠ABC = 2×m∠ABD = 2×8

m∠ABC = 16

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We presume the angle measures are in degrees, though that is not specified by the problem given here. These numbers could all be radians, but 16 radians is more than a couple of times around the circle.